Thus, \({\left\Vert  {{{\bf {h}}_k}{{\bf {w}}_k}} \right\Vert ^2}\)  follows the distribution of sum of \(N_T\)  Fisher-Snedecor \(\mathcal {F}\)  RVs [1]}. However, the PDF and CDF of \({\left\Vert  {{{\bf {h}}_k}{{\bf {w}}_k}} \right\Vert ^2}\)  is in terms of Multivariate Fox's \(H\) -function [2]}, which is hard to provide insights. Considering that the Fisher-Snedecor \(\mathcal {F}\)  RV is defined as the ratio of two Gamma RVs and the sum of Gamma RVs still follows the Gamma distribution, we can use the single Fisher-Snedecor \(\mathcal {F}\)  distribution to approximate the distribution of the sum of Fisher-Snedecor \(\mathcal {F}\)  RVs [1]}.
